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Physics-04 (Leph_20903)

Physics 2019 Physics-04 (Leph_20903) Ray Optics and Optical Instruments

1. Details of Module and its structure

Subject Name Physics

Course Name Physics 04 (Physics Part 2, Class XII)

Module Name/Title Unit- 06, Module- 03: Phenomenon of refraction, Refraction

through a glass slab,

Chapter-09: Ray Optics and Optical Instruments

Module Id leph_20903_eContent

Pre-requisites Light, sources of light, transparent and opaque objects, ray of

light, parallel beam, converging beam , diverging beam, real

image , virtual image, incident ray

Objectives After going through this module, the learners will be able to:

Understand Refraction

Distinguish between mass density and optical density

Define refractive index of a medium and relate refractive

index of a medium with the speed of light in the medium

Trace the path of an oblique ray of light through a rectangular

glass slab.

Predict the effects of change in (i) angle of incidence, (ii)

thickness of glass slab and (iii) the refractive index of the

material of the slab, on the lateral displacement produced in

the incident ray.

Keywords Refraction, refractive index, lateral displacement, Snell’s law,

optical density

2. Development Team

Role Name Affiliation

National MOOC

Coordinator (NMC)

Prof. Amarendra P. Behera Central Institute of Educational

Technology, NCERT, New Delhi

Programme Coordinator Dr. Mohd Mamur Ali Central Institute of Educational


Course Coordinator / PI Anuradha Mathur Central Institute of Educational


Subject Matter Expert

(SME)

Pushpa Vati Tyagi Retired (Kendriya Vidyalaya

Sangathan)

Review Team Associate Prof. N.K. Sehgal

(Retd.)

Prof. V. B. Bhatia (Retd.)

Prof. B. K. Sharma (Retd.)

Delhi University

Delhi University

DESM, NCERT, New Delhi



TABLE OF CONTENT

1. Unit Syllabus

2. Module wise distribution of unit syllabus

3. Words you must know

4. Introduction

5. Optical density and mass density

6. Incident ray, refracted ray and emergent ray, angle of incidence, angle of refraction and

angle of emergence

7. Refractive index

8. Oblique incidence of light and Snell’s law

9. Refraction through a parallel sided glass slab, lateral displacement; factors affecting lateral

displacement

10. To observe refraction, and lateral displacement, of a beam of light incident obliquely on a

glass slab

11. Formation of image in a glass slab

12. Intensity of refracted light -To use a LDR to study the variation in the intensity of light,

emerging through different coloured transparent sheets

13. Summary

1. UNIT SYLLABUS

UNIT 6

Chapter–9: Ray Optics and Optical Instruments

Ray optics Reflection of light; spherical mirrors; mirror formula; refraction of light; total

internal reflection and its applications; optical; fibers; refraction at spherical surfaces; lenses;

thin lens formula; lens maker’s formula; magnification, power of a lens; combination of thin

lenses in contact; refraction and dispersion of light through a prism.

Scattering of light – blue color of sky and reddish appearance of the sun at sunrise and sunset

Optical instruments – microscopes and astronomical telescopes (refracting and reflecting) and

their magnifying powers

Chapter 10 Wave Optics

Wave optics: wave front and Huygens’s principle, reflection and refraction of plane wave at a

plane surface using wave fronts, proof of laws of reflection and refraction using Huygens’s

principle. Interference, Young’s double slit experiment and expression for fringe width,

coherent sources and sustained interference of light; diffraction due to a single slit width of

central maximum; resolving power of microscope and astronomical telescope. Polarisation,

plane polarised light, Malus’s law, Brewster’s law, uses of plane polarised light and polaroid.



2. UNIT WISE MODULE DISTRIBUTION OF UNIT SYLLABUS 15 MODULES

Module 1

Introduction

How we will study optics-plan

Light facts

Ray optics, beams

Light falling on surfaces of any shape texture

Peculiar observations

Module 2

Reflection of light

Laws of reflection

Reflection of light by plane and spherical surfaces

Spherical Mirrors aperture, radius of curvature, pole

principal axis

Focus, Focal length, focal plane

Image – real and virtual

Sign convention

The mirror equation, magnification

To find the value of image distance v for different values of

object distance u and find the focal length of a concave

mirror

Application of mirror formula

Module 3

Refraction of light

Optical density and mass density

Incident ray, refracted ray emergent ray

Angle of incidence, angle of refraction angle of emergence

To study the effect on intensity of light emerging through

different colored transparent sheets using an LDR

Refractive index

Oblique incidence of light, Snell’s law

Refraction through a parallel sided slab

Lateral displacement,

Factors affecting lateral displacement

To observe refraction and lateral displacement of a beam of

light incident obliquely on a glass slab

Formation of image in a glass slab

Module 4

Special effects due to refraction

Real and apparent depth



To determine the refractive index of a liquid using travelling

microscope

Total internal reflection

Optical fibers and other applications

Module 5

Refraction through a prism

Deviation of light -angle of deviation

Angle of minimum deviation

Expression relating refractive index for material of the

prism and angle of minimum deviation

To determine the angle of minimum deviation for given

prism by plotting a graph between angle of incidence and

angle of deviation

Dispersion, spectrum

Module 6

Refraction at spherical surfaces

Radius of curvature

Refraction by a lens

Foci, focal plane, focal length, optical center, principal axis

Formation of images real and virtual

Lens maker’s formula

Lens formula and magnification

Sign convention

Application of lens formula

Power of lens

Combination of thin lenses in contact

Module 7

To study the nature and size of image formed by a

convex lens

ii) concave mirror using a candle and a screen

To determine the focal length of convex lens by plotting

graphs between u and v, between 1/u and 1/v

To determine the focal length of a convex mirror using a

convex lens

To find the focal length of a concave lens using a convex lens

To find the refractive index of a liquid by using a convex lens

and a plane mirror

Module 8

Scattering of light –

Blue color of sky

Reddish appearance of the sun at sunrise and sunset



Dust haze

Clouds

Module 9

optical instruments

human eye

microscope

astronomical telescopes reflecting and refracting

magnification

making your own telescope

Module 10

wave optics

wave front

Huygens’s principle shapes of wave front

plane wave front

Refraction and reflection of plane wave front using

Huygens’s principle

Verification of Laws of refraction and reflection of light

using Huygens’s principle

Module 11

Superposition of waves

Coherent and incoherent addition of waves

Module 12

Interference of light

Young’s double slit experiment

Expression for fringe width

Graphical representation of intensity of fringes

Effect on interference fringes in double slit experiment

Black and white or colored fringes

Module 13

Diffraction

Diffraction at a single slit,width of the central maxima

Comparison of fringes in young’s experiment and those in

diffraction from a single slit

Module 14

Diffraction in real life

Seeing the single slit diffraction pattern

Resolving power of optical instruments

Validity of ray optics

Fresnel distance

Module 15

Polarisation

to observe polarization of light using two polaroid

Plane polarised light



Polariser analyser Malus law

Brewster/s law

Polarisation due to scattering

Uses of plane polarised light and polaroids

3. WORDS YOU MUST KNOW

Let us remember the words and the concepts we have been using in our study of light

Light: Light is a form of energy which gives the sensation of vision when it falls on the

retina of the eye.

Ray of light: The straight line path along which light travels is called a ray of light. Light

rays start from each point of a source and travel along straight line until they strike an object

or a surface separating two media.

Beam of light: A group of rays of light is called a beam of light.

Parallel beam of light: If all the rays of light in the group are parallel to each other than

the beam is said to be a parallel beam of light.

Converging beam of light: If the rays of light in the group come closer to each other i.e.

converge to a point, then the beam is said to be a converging beam of light.

Diverging beam of light: If the rays of light in the group move away from each other i.e.

diverge, then the beam is said to be a diverging beam of light.

Transparent medium: A medium through which light can pass freely over large distance

is called a transparent medium. Glass and still water are some examples of transparent

objects

Opaque medium: A medium through which light cannot pass is called an opaque medium.

Wood and metals are some examples of opaque objects.

Real image: If the rays of light after reflection from a mirror actually meet at a point i. e.

the reflected beam is a converging beam, then the image is said to be real image.

Virtual image: If the rays of light after reflection from a mirror do not actually meet at a

point but seem to come from a point behind the mirror i.e. the reflected beam is a diverging

beam, then the image is said to be a virtual image.

Ray diagram A diagram that traces the path that light takes in order for a person to view a point

on the image of an object. On the diagram, rays (lines with arrows) are drawn for the incident ray

and the reflected ray or refracted

Spherical surface any surface which is a part of a sphere



Pole: - The geometrical center of the surface of the mirror is called its pole. It is marked as

point (p) in the diagram.

Centre of curvature: - It is the center of the hollow sphere of which the mirror is a part. It is

marked as point (C) in the diagram.

Radius of curvature: - It is the radius of the sphere of which the mirror is a part.

Principal axis: - The line joining the pole and the center of curvature of the mirror is called its

principal axis.

Aperture of a mirror:- The diameter of the circular cross section of the sphere, used to form

the spherical mirror is called its aperture

Focus point focal plane: - a parallel beam of light parallel to the principal axis; is incident on

a concave or a convex mirror. The reflected rays are observed to converge to a point on the

principal axis in case of a concave mirror; or they appear to diverge from a point on the

principal axis in case of a convex mirror. This point of convergence or apparent convergence

is called the focus point (F). . and the plane containing the focus perpendicular to the principal

axis is called the focal plane.

Focal length the distance from the pole to the focus is called focal length.

Object distance (u) the distance of the object from the pole

Image distance (v) the distance of the image from the pole

Sign convention a universally accepted convention based on Cartesian coordinate system to

indicate the location of object and image with respect to a mirror surface

Mirror formula An equation which expresses the quantitative relationship between the

object distance ( u), the image distance ( v), and the focal length (f). The equation is stated as

follows:

1

𝑓=

1

𝑣+

1

𝑢

magnification the ratio of the image distance and object distance to the ratio of the image

height ( I) and object height ( O). The magnification equation is stated as follows:



m =height of image

height of object=

image distance

object distance

4. INTRODUCTION:

We have seen that when light falls on a surface it gets reflected and follow the laws of

reflection of light.

Light seems to travel along straight-line paths in a transparent medium.

What happens when light enters from one transparent medium to another?

Does it still move along a straight-line path or change its direction? We shall recall some

of our day-to-day experiences. Have you seen a pencil partly immersed in water in a glass

tumbler? It appears to be displaced at the interface of air and water. You might have

observed that a lemon kept in water in a glass tumbler appears to be bigger than its actual

size, when viewed from the sides. How can you account for such experiences?

You might have observed that the bottom of a bucket, tank or a pond containing water

appears to be raised. Similarly, when a thick glass slab is placed over some printed matter,

the letters appear raised when viewed through the glass slab. Why does it happen?

The red arrow shows the path of light as it propagates through the glass slab

https://upload.wikimedia.org/wikipedia/commons/8/85/Refraction_photo.png

Now we will see what happens to the path of a ray of light when it goes from one transparent

medium to another transparent medium.

5. REFRACTION OF LIGHT:

Let a laser beam fall normally on a glass slab, you will see that it passes straight through

the slab. Next increase the angle of incidence you will see that the beam of light has

deviated from its path.

https://upload.wikimedia.org/wikipedia/commons/8/85/Refraction_photo.png



Video light box activities

The phenomenon of bending of incident light from its path when it goes from one

transparent medium to another transparent medium is (usually) called the

refraction of light.

This ‘bending’ takes place because of a change in the speed of light as it goes from

one medium to another.

We may, therefore, (preferably) say:

“The phenomena, associated with a ray of light, due to a change in its speed, make

up the phenomena of refraction.

The bending of path, of an obliquely incident ray of light, in going from one transparent

medium to another, is the most common, and easily observed, effect of refraction.



So to see both reflection and refraction of light consider the figure

Note

At the point of incidence, the normal, reflected ray and refracted ray

The refracted ray can be seen to bend towards the normal

In order to understand the cause of this bending of light on refraction, let us first

understand the difference between mass density and optical density

6. MASS DENSITY AND OPTICAL DENSITY:

Mass density:

Mass density is defined as mass per unit volume of the substance.

Mass density= 𝑚𝑎𝑠𝑠

𝑣𝑜𝑙𝑢𝑚𝑒

Now, what is meant by the statement density of water is 1000 kg per meter3

It means 1 m3 of water contains 1000 kg of water

Optical density:-

The ability of a medium to refract light is also expressed in terms of its optical density.

Optical density has a definite connotation. It is not the same as mass density. We have been

using the terms ‘rarer medium’ and ‘denser medium’. It actually means ‘optically rarer

medium’ and ‘optically denser medium’, respectively.

When can we say that a medium is optically denser than the other?

The speed of light is higher in a rarer medium than a denser medium.



Thus, a ray of light travelling from a rarer medium to a denser medium slows down

and bends towards the normal. When it travels from a denser medium to a rarer

medium, it speeds up and bends away from the normal.

So, as light travels from one transparent medium to another transparent medium its speed

changes. If, on entering the second medium, the speed of light decreases then this second

medium in which light has entered is said to have more optical density than that of the first

medium.

In other words, an increase in ‘optical density’ implies a decrease in speed of light and

vice – versa.

For a given pair of medium, the medium in which light propagates faster is the optically

rarer medium and the medium in which light propagates slower, is the optically denser

medium of that pair.

Optical density, may, therefore, be regarded as determining the speed of light in a given

medium.

Optical density should therefore, not be confused with mass density,which is mass per

unit volume

It is quite possible that the mass density of an optically denser medium can be less

than that of an optically rarer medium.

For example, turpentine has less mass density than water.

However, since light propagates slower in it than in water, i.e. it has more optical

density than water. The phenomena of ‘refraction’

7. INCIDENT RAY, REFRACTED RAY AND EMERGENT RAY

ANGLE OF INCIDENCE, ANGLE OF REFRACTION AND ANGLE OF

EMERGENCE

Refraction through a rectangular glass slab

Incident ray: - The ray of light which strikes the surface of separation of two media is

called incident ray. .

Point of incidence: - The point at which the incident ray strikes the interface of the two

media is called point of incidence.

Angle of incidence: - The angle which the incident ray makes with the normal drawn at

the point of incidence is called the angle of incidence. Angle marked as i in the diagram is

angle of incidence.



Refracted ray: - The ray of light which travels into the second medium is called refracted

ray. It is represented by ray QR in the figure.

Angle of refraction: - The angle, which the refracted ray makes with the normal drawn at

the point of incidence is called the angle of refraction. Angle N’QR is angle of refraction;

it is usually represented as angle r.

At point of first refraction

Angle of incidence =i1

Angle of refraction = r1

At the second point of refraction

Angle of incidence =i2

Angle of refraction = r2

An incident ray at the first surface undergoes refraction from air (medium 1 ) to glass

(medium 2) or rarer to denser medium

The second refraction takes place at the point of emergence ray travels from denser

to rarer medium

Emergent ray the ray emerging from a medium is called emergent ray, it is the

refracted ray emerging from a medium

Lateral shift or lateral displacement– light emerging from a in a parallel sided

medium like a glass slab or water in a flat bottomed container (glass) held with the base

horizontal, the emergent ray shifts from its original direction. The shift is sideways

hence called lateral shift.

Deviation of emergent light-



Light its path on refraction the angle of deviation = angle of incidence - angle of

refraction

Light emerging from a non-parallel sided medium deviates from its original path

Deviation of light at the first interface = i1 - r1

At the second point of refraction deviation = r2-i2



THINK ABOUT THESE

check it out from the light box activity video



WATCH THE VIDEO LIGHT BOX

8. REFRACTIVE INDEX:-

Speed of light in a medium depends upon the properties of that medium. We have seen

above that it depends upon the optical density of the medium. The more optically dense a

given medium is, the less is the speed of light in that medium. The optical density of a

medium is indicated by a term called, the refractive index of that medium.

Refractive index of a medium is a number which indicates the factor by which the speed

of light, in that medium, gets reduced with respect to its speed in vacuum. In comparing

two media, the one with the larger refractive index is optically denser medium than

the other. The other medium of lower refractive index is optically rarer.

We define it as follows:

Refractive index of a medium = n

=𝐬𝐩𝐞𝐞𝐝 𝐨𝐟 𝐥𝐢𝐠𝐡𝐭 (𝐜 )𝐢𝐧 𝐯𝐚𝐜𝐮𝐮𝐦

𝐬𝐩𝐞𝐞𝐝 𝐨𝐟 𝐥𝐢𝐠𝐡𝐭 (𝐯)𝐢𝐧 𝐭𝐡𝐞 𝐦𝐞𝐝𝐢𝐮𝐦



𝑛 =𝑐

𝑣

Relative refractive index: - Consider light going from medium 1 to medium 2

Relative refractive index of medium 2 with respect to medium 1 is

𝑛21 =𝑛2

𝑛1

Or

𝑛21 =𝑐/𝑣2

𝑐/𝑣1

or

𝑛21 =𝑣1

𝑣2

For example: refractive index of glass with respect to water =1.5

𝐧𝐠

𝐧𝐰=

𝐯𝐰

𝐯𝐠

Velocity of light in water is greater than, that, in glass

EXAMPLE

Refractive index of glass is 1.5. Find the speed of light in glass. Given: the speed of

light in vacuum = 3x108 m/s)

SOLUTION

We have

𝑛 =𝑐

𝑣

So 1.5 = 3x108/v

V = 2 x 108 m/s

EXAMPLE

Refractive index of glass is 3/2 and refractive index of water is 4/3.

a) Find the refractive index of glass w.r.t. water.

b) The ratio of speed in water as compared to speed in glass

SOLUTION

Refractive index of glass with respect to water =



𝑛𝑔𝑤 =𝑛𝑔

𝑛𝑤=

𝑣𝑤

𝑣𝑔

= (3/2)/( 4/3) = 9/8

If n21 is the refractive index of medium 2 with respect to medium 1 and n12 the

refractive index of medium 1 with respect to medium 2, then it should be clear that

𝒏𝟐𝟏 =𝟏

𝒏𝟏𝟐

It also follows that if n32 is the refractive index of medium 3 with respect to medium 2

Then

n32 = n31 × n12,

Where, n31 is the refractive index of medium 3 with respect to medium 1.

Some elementary results based on the laws of refraction follow immediately, like the

displacement from a parallel sided glass slab, the bottom of a tank filled with water

appears raised!

9. LAWS OF REFRACTION OF LIGHT: -

When a beam of light encounters another transparent medium, a part of light gets reflected

back into the first medium while the rest enters the other. A ray of light represents a beam.

The direction of propagation of an obliquely incident ray of light that enters the other

medium, changes at the interface of the two media.

Snell experimentally obtained the following laws of refraction:

(i) The incident ray, the refracted ray and the normal to the interface at the point of

incidence, all lie in the same plane.

(ii) The ratio of the sine of the angle of incidence to the sine of angle of refraction is

constant. Remember that the angles of incidence (i) and refraction (r) are the

angles that the incident and its refracted ray make with the normal, respectively.

We have

𝐧𝟐𝟏 =𝐬𝐢𝐧 𝐢

𝐬𝐢𝐧 𝐫

𝐧𝟐

𝐧𝟏=

𝐬𝐢𝐧 𝐢

𝐬𝐢𝐧 𝐫

𝐧𝟏𝐬𝐢𝐧𝐢 = 𝐧𝟐𝐬𝐢𝐧𝐫



CAUSE OF BENDING OF LIGHT DUE TO REFRACTION : -

We know that light propagates with different speeds in different media. When a ray of

light goes from one medium to another it bends its path because of change in its speed.

The more is the change in speed of light, as it goes from one medium to another; more

will be the bending in its path.

According to Snell's law

𝒏𝟐

𝒏𝟏=

𝒔𝒊𝒏 𝒊

𝒔𝒊𝒏 𝒓=

𝒗𝟏

𝒗𝟐

When light goes from a rarer medium to a denser medium, its speed decreases i.e.

v2< v1.

Hence i > r

This means that a ray of light, incident obliquely, will bend towards the normal when

it goes from an optically rarer medium to an optically denser medium.

When light goes from an optically denser medium to an optically rarer medium,

its speed increases i.e. v1< v2.

Hence i < r

This means that a ray of light, incident obliquely, will bend away from the normal when

it goes from an optically denser medium to an optically rarer medium.

Note: -

When a ray of light, incident obliquely, moves from an optically rarer medium to an

optically denser medium it moves towards the normal.

When a ray of light, incident obliquely, moves from an optically denser medium to an

optically rarer medium it moves away from the normal.

If light moves from rarer to denser medium, angle of refraction is less than angle of

incidence

If light moves from denser to rarer medium, angle of refraction is more than angle of

incidence

Effect of refraction on the wavelength and frequency of the incident light:-

When a ray of monochromatic light (light of a single frequency) goes from one medium

to another, its speed changes. However, there is no change in its frequency, which

may be regarded as a characteristic of the source.

Now v= f λ (where λ is wavelength and f is frequency of light).



Hence for the two media

v1= fλ1

v2= fλ2

𝒏𝟐𝟏 =𝒏𝟐

𝒏𝟏=

𝒔𝒊𝒏 𝒊

𝒔𝒊𝒏 𝒓=

𝒗𝟏

𝒗𝟐

So the frequency remains the same but wavelength changes. We will study this in

greater detail in later modules of optics

EXAMPLE: -

Refractive index of glass is 3/2 and refractive index of water is 4/3. If the speed of

light in water is 2.25 x 10 8m/s, find the speed of light in glass.

SOLUTION: -

Refractive index of glass with respect to water = 𝑛𝑔

𝑛𝑤=

𝑣𝑤

𝑣𝑔

vg = vw (nw

ng) =

4

3×

2

3× 2.25 × 108ms−1 = 𝟏. 𝟗𝟓 × 𝟏𝟎𝟖𝐦𝐬−𝟏

EXAMPLE: -

A ray of light is incident normally on a glass surface. Show that it will not bend

from its path.

SOLUTION: -

For the normally incident ray, we have angle i= 0

According to Snell’s law

n1sin i= n2 sin r

n1sin 0 = n2 sin r

0 = n2 sin r

Since n2 is not equal to zero

We would have

𝑠𝑖𝑛 𝑟 = 0



Thus 𝑟 = 0

Hence there is no change in the path of the normally incident light ray. In other

words, the ray of light will not bend when it is incident normally.

EXAMPLE:-

Show that the refractive index of medium 2 w.r.t. medium 1 is reciprocal of the

refractive index of medium 1 w.r.t. medium 2

SOLUTION:

Consider a ray of light AB going from medium 1 to medium 2. The ray AB is incident

on a plane surface PQ separating the two media. Let the medium 1 be a rarer medium

and the medium 2, a denser medium. It will bend towards the normal, so

BC is the refracted ray.

According to laws of refraction of light

n21= sin i /sin r

Suppose the path of the ray BC is reversed by placing a plane mirror normal to BC.

Now angle of incidence = angle CBN’ = r,

and angle of refraction = angle NBA= i

According to laws of refraction of light

n12 = sin r /sin i

n21 x n12 = (sin i/sin r ) x (sin r /sin i) =1

Thus n21= 1/ n12



EXAMPLE

Select the correct placing of the protractor to measure the angle of incidence on a

glass slab

SOLUTION

B Angle of incidence is the angle between the incident ray and the normal

10. REFRACTION THROUGH A PARALLEL SIDED GLASS SLAB, LATERAL

DISPLACEMENT AND FACTORS AFFECTING LATERAL DISPLACEMENT; -

Consider a rectangular glass slab of thickness (t). A ray of light PQ, propagating in air

strikes the interface of air and glass at an angle of incidence ‘i’. As light is going from a

rarer to a denser medium, it turns bends towards the normal and moves along QR. The

angle N’QR is angle of refraction ‘r’.

As the two opposite faces of the rectangular glass slab are parallel to each other, the

refracted ray QR strikes the surface DC at an angle of incidence equal to ‘r’. Now as light

is going from glass to air i.e. from a denser medium to a rarer medium, it bends away from

the normal. The ray of light QR which comes out of the glass slab after refraction is called



the ‘emergent ray’. The emergent ray QR is parallel to the incident ray as the two

refracting surfaces are also parallel to each other.

Thus the angle of incidence = angle of emergence

On producing the incident ray PQ, we will see that it is parallel to the emergent ray but

displaced laterally. From the point R drop perpendicular RT on the produced incident ray.

RT is called the lateral displacement produced by the glass slab placed in the path of the

(obliquely incident -making an angle with the normal at the point of incidence) light ray.

The perpendicular distance, between the incident ray and the emergent ray, when light is

incident obliquely on a parallel sided glass slab, is called lateral displacement or lateral

shift.

EXPRESSION FOR LATERAL SHIFT: -

In right angled triangle QTR,

∠𝑇𝑄𝑅 = (𝑖 − 𝑟)

𝑆𝑖𝑛 (𝑖 − 𝑟 ) = (𝑅𝑇/𝑄𝑅) = 𝑑/𝑄𝑅,

Where d = RT, is lateral displacement

Thus 𝑑 = 𝑄𝑅 𝑠𝑖𝑛 (𝑖 − 𝑟)

In right angle triangle N’QR, we have

𝑐𝑜𝑠 𝑟 = (𝑄𝑁’/ 𝑄𝑅 ) = 𝑡/𝑄𝑅



S0, 𝑄𝑅 = (𝑡/𝑐𝑜𝑠 𝑟)

Substituting the value of QR we get

𝒅 = 𝒕 (𝒔𝒆𝒄 𝒓) 𝒔𝒊𝒏 ( 𝒊 − 𝒓)

This expression leads us to conclude that the lateral shift, produced by a rectangular glass slab,

increases with

Increase in thickness of the glass slab

Increase in angle of incidence

Increase in refractive index of the glass used for making the slab

TO OBSERVE REFRACTION AND LATERAL DISPLACEMENT OF A BEAM OF

LIGHT INCIDENT ON A GLASS SLAB: -

i) Fix a white sheet paper on a drawing board.

To ensure that the paper does not move accidently and is firmly fixed

ii) Draw a line parallel to the length of the paper, mark a point Q on it

To get more space for the experiment

iii) Draw normal at Q ,NQN’

iv) Put the glass slab along the line adjusting the point Q to be about 2 cm from edge

A and draw its boundary A B C D with a sharp pencil. The boundary is marked

so that we can place the glass slab on the same position.

v) Draw a line PQ, making an angle, say 45 0, with normal. This angle will be the angle

of incidence.

vi) Fix two pins (pin 1 and 2), on the line PQ, 2 to 3 cm apart from each other, and also

from the glass slab. Ensure that the pins are vertical.



vii) See the image of the lower ends of the pins from the face CD and fix two more pins

(pin 3 and pin 4) such that the lower ends of all the four pins lie along a straight

line.

viii) Ensure that these two pins are also 2 to 3 cm apart from each other and

also the glass slab. This is to ensure that you see along the line joining the two

pins, this line is the ray represented by the pins and you see through the slab

The images of the pins should be seen and not the pins

To trace the emergent ray, we need to see along the line through the glass slab,

we must also close one eye and trace the rays with only one eye

ix) Remove the pins and encircle the pin pricks.

This is done to mark the location of the fine hole created by the pin.

x) Remove the glass slab and join the pin pricks (3) and (4).

This line/ray will represent the emergent ray; the point of emergence is R

xi) Join QR to represent the refracted ray.

xii) Draw normal at the point R on the face CD

xiii) Measure the angle of refraction N’QR = r

xiv) Measure the angle of emergence e.

xv) Produce PQ. Draw RT perpendicular to QU.

xvi) RT is the lateral displacement

xvii) We will see that

∠ 𝒊 = ∠𝒆

∠ 𝑰 > ∠ 𝒓

Incident ray PQ is laterally displaced.

xviii) Find the value of the ratio (sin i/ sin r).

This gives the refractive index of the glass used for making the given slab.

https://www.youtube.com/watch?v=KuCUaE6e1Oo

EXAMPLE

Draw ray diagrams to show that the lateral shift produced by a thick glass slab is

greater than a thin glass slab

SOLUTION

https://www.youtube.com/watch?v=KuCUaE6e1Oo



11. FORMATION OF IMAGE IN A GLASS SLAB: -

When we look through a glass bottle filled with water you see images of objects

and not the objects.

We see the image of the fish in a glass bowl

Let us use ray optics to show the formation of image

Consider a glass slab PQRS of thickness t placed on a thick white paper kept on a look

from above almost normally, we will see the image I.

Let us first try to understand the formation of image



The ray of light OA strikes normal to the surface and goes straight without bending as

its angle of incidence is zero degree.

The ray of light OB, which strikes the interface obliquely, will go away from normal

as it is going from denser medium to a rarer medium.

Both the refracted rays appear to come from the point I;

The point I is the virtual image of the object O.

We see that the object point O seems to be raised, when viewed through a glass slab.

EXAMPLE

A light ray goes from the air into the water. If the angle of incidence is 340

What is the angle of refraction?

SOLUTION

nwa =sin i

sin r=

sin 34

sin r

𝑠𝑖𝑛𝑟 =sin 34

1.33=

0.529

1.33= 0.397

angle of refraction r = sin-1 0.397 = 23.30



EXAMPLE

Reena stands at the edge of a swimming pool 3.0 m deep. She shines a laser at a

height of 1.7m. The laser beam strikes the water surface of the pool 8.1 m from the

source.

a) Draw a diagram of this situation. Label all known lengths.

b) How far from the edge of the pool will the light hit bottom?

SOLUTION

Hint- Calculate the angle of incidence

Angle of refraction

Distance of point of strike of laser beam on the base of the pool

TRY THIS

You are to design an experiment to determine the index of refraction of an unknown

liquid. You have a small square container of the liquid, the sides of which are made of

transparent thin plastic. In addition you have a screen, laser, ruler and protractors.

Design the experiment. Give a detailed procedure; include a diagram of the experiment.

Tell which equations you would use and give some sample calculations. Finally, tell in

detail what level of accuracy you can expect and explain the causes of lab error.

12. USE A LDR TO STUDY THE VARIATION IN THE INTENSITY OF LIGHT,

EMERGING THROUGH DIFFERENT TRANSPARENT SHEETS OF

DIFFERENT COLOURS.

Apparatus required: -

LDR( light dependent resistance

multimeter,

100W bulb,



transparent colourless sheet,

transparent sheets of different colours (cellophane paper)

Principle The intensity of light decreases on refraction as the medium absorbs some

energy

Procedure:

(i) Set the multimeter to measure resistance.

(ii) Connect the given LDR to the multimeter.

(iii)Fix the bulb at a distance of about 50cm from the LDR.

(iv) Switch the bulb on,and note down the resistance from the multimeter.

(v) Insert the colourless transparent sheet in between the bulb and the LDR.

(vi) Again note down the value of resistance from the multimeter.

(vii) Do you see any change in the value of the resistance?

(viii) If yes, try to explain it.

(ix) Replace the colourless transparent sheet with a blue colour transparent sheet of the

same thickness as the colourless sheet and at the same position.

(x) Note down the value of the resistance from the multimeter.

(xi) Repeat the steps 9 and 10 with transparent sheets of different colours.

(xii) Prepare a table showing the colour of thin sheet and the corresponding

resistance.

(xiii) Analyze the data you have collected.

You may use the FUN activity as project as also study the variation in intensity of

light emerging from a glass slab with angle if incidence.

13. SUMMARY:-

The phenomenon, of bending of incident light from its path when it encounters another

transparent medium is called refraction of light.



The phenomenon, associated with the change in speed of light as it goes from one

medium to another.

For a given pair of media, the medium in which light propagates faster, is called

optically rarer medium and the medium in which light propagates slower, is called

optically denser medium

When a ray of light, incident obliquely, moves from an optically rarer medium to an

optically denser medium, it bends towards the normal.

When a ray of light, incident obliquely, moves from an optically denser medium to an

optically rarer medium, it bends away from the normal.

When a ray of light goes from an optically rarer to an optically denser medium, angle

of refraction is less than the angle of incidence

When a ray of light goes from an optically denser to an optically rarer medium, angle

of refraction is more than the angle of incidence.

Laws of refraction of light: -

i) The incident ray, the refracted ray, and the normal at the point of incidence, all lie

in the same plane.

ii) The ratio, of the sine of the angle of incidence to the sine of the angle of refraction

r, for a given pair of two media is constant for a given wavelength of light; it is equal

to the refractive index of the second medium with respect to first medium. We call this

law as Snell’s law.

We can put Snell’s law in the mathematical form:

n1 sin I = n2 sin r

When a ray of light passes through a parallel sided glass slab,

i) The emergent ray is parallel to the incident ray, i.e., the angle of incidence = angle of

emergence

The emergent ray is laterally displaced. The lateral shift, produced by a glass slab

increases with

Increase in thickness of the glass slab

Increase in angle of incidence

Increase in refractive index of the glass used for making the slab

When a ray of light undergoes refraction through a combination of three media i.e. air,

water and glass (all boundaries are parallel planes) , then



𝑛𝑤𝑎 × 𝑛𝑔𝑤 × 𝑛𝑎𝑔 = 1

𝑜𝑟 𝑛𝑔𝑤 =𝑛𝑔𝑎

𝑛𝑤𝑎

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